Best Known (49, 88, s)-Nets in Base 16
(49, 88, 524)-Net over F16 — Constructive and digital
Digital (49, 88, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 44, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(49, 88, 646)-Net over F16 — Digital
Digital (49, 88, 646)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(1688, 646, F16, 2, 39) (dual of [(646, 2), 1204, 40]-NRT-code), using
- trace code [i] based on linear OOA(25644, 323, F256, 2, 39) (dual of [(323, 2), 602, 40]-NRT-code), using
- construction X applied to AG(2;F,600P) ⊂ AG(2;F,604P) [i] based on
- linear OOA(25641, 320, F256, 2, 39) (dual of [(320, 2), 599, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,600P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- linear OOA(25637, 320, F256, 2, 35) (dual of [(320, 2), 603, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,604P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321 (see above)
- linear OOA(2563, 3, F256, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2563, 256, F256, 2, 3) (dual of [(256, 2), 509, 4]-NRT-code), using
- Reed–Solomon NRT-code RS(2;509,256) [i]
- discarding factors / shortening the dual code based on linear OOA(2563, 256, F256, 2, 3) (dual of [(256, 2), 509, 4]-NRT-code), using
- construction X applied to AG(2;F,600P) ⊂ AG(2;F,604P) [i] based on
- trace code [i] based on linear OOA(25644, 323, F256, 2, 39) (dual of [(323, 2), 602, 40]-NRT-code), using
(49, 88, 172464)-Net in Base 16 — Upper bound on s
There is no (49, 88, 172465)-net in base 16, because
- 1 times m-reduction [i] would yield (49, 87, 172465)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 573 388488 904646 250554 707326 283893 604818 256838 618537 660384 986641 158100 704879 944083 334676 202675 815237 015776 > 1687 [i]